The Slaveboy

I was working out a math problem and Abi asked me what I was doing. I said, "It's geometry", which of course elicited the question, "What's that?"

So I drew a square subdivided into four smaller squares and said, "Look, this big square is four times as big as the little ones. Can you draw a square that's only twice as big as the little ones?"

She first drew a 2 x 1 rectangle subdivided into two squares; I pointed out this wasn't a square. Then she drew a square subdivided into two rectangles; I pointed out they weren't squares. Then she gave up and wanted me to tell her the answer.

I showed her Socrates' answer -- connect the midpoints of the large square -- and asked her why it works. She pointed to the eight triangles. I'm not sure she fully got it on her own, but we went over it together: How many triangles in the smaller square? How many in the larger square? I think she more or less got it.

Her other mathematical accomplishments of late include adding two-digit numbers without carry (with no help at all); multiplying 12 by 4 and by 5 (with minor prompting from Josh); and figuring out that "4 years and 3/4" means "4 years and 9 months" (with minor prompting from me).